Foot and Mouth
Disease (FMD) outbreak in UK 2001 is analysed with logistic
equation models showing how poorly the outbreaks were controlled.
Includes an historical review of the disease as it
unfolded.

Forecasting & Reviewing
Foot & Mouth Disease Control

An outbreak of foot and mouth disease (FMD) occurred in the
United Kingdom in February 2001. Logistic
equations have been commonly applied to the study of population
dynamics. How well do they apply to growth in foot and mouth cases
? Are they useful in predicting the impact of an epidemic, or
reviewing it's control ? How do they compare with the more complex
epidemiologist's models used by the UK Chief Scientist ? (jump to
answer if you're impatient)? Why did this
outbreak last so much longer than the 1967 one ?

This page was updated daily through the course of the FMD
outbreak.
Modifications are dated. Some revisions in early material were
made as new information came to light.

Last revised 6th October 2001, first published 12th April,
2001.

The first sections below focus on predicting the course of the
FMD outbreak in the period before 26th April, as an aid to
understanding the effectiveness of control measures. As the
evidence from hindsight eventually showed, control of the outbreak
weakened enormously shortly after 26th April. For the period April
through until the end of September, the best prediction of the
outbreak's future course was that it would not end (see Figure's 1 and 12 below).
Fortunately, by the 6th October, evidence had emerged that the
epidemic had at long last come to an end (see Figure 14 below). The last reported case was in fact 30th
September, 2001

With the benefit of hindsight, it can be seen that a logistic
model fits the outbreak data very well in the initial stages where
there was an explosive growth then sharp decline in daily cases
reported. But as the new cases per day fell below 5 per day, there
was a period of almost constant growth. This suggests some
complacency or level of acceptance crept into the fight against the
disease in what should have been its end-phase. As a consequence,
perhaps more than a 1000 culled farms could have been saved.

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The simplest model of growth assumes that a
population grows in proportion to its size. Both the birth rate and
death rates in such a model are proportional to the population
size. This results in a never-ending exponential growth.

Fortunately, reality is usually different. While initially a
population might appear to explode exponentially, at some point it
will begin to exhaust resources, and death rates will grow more
quickly than in proportion to the population size.

The logistic equation is the simplest model for growth that
allows the growth rate to reach zero at some point in time. This is
achieved by assuming that death rates grow in proportion to the
square of the population size (for the mathematicians, it uses the
first two terms of a Taylor series expansion, see here for more details).

Consider an example with a birth rate of
20% of the population, and death rate of 1% of the
population-squared: with 10 infected farms, you might have a
potential to have 2 new infected farms (20% of 10), but one of
these is prevented (1% of 10 * 10) by controls. With 20 infected
farms, the potential is to have 4 new infected farms (20% of 20),
but all 4 are suppressed (1% of 20 * 20 = 4).

Under these assumptions, the population will grow to a
particular limit at which the birth rates and death rates match;
this limit (or asymptote) turns out to be the birth rate divided by
the death rate (see Logistic
equations for a more mathematical treatment).

The Logistic equation models growth of populations in which a
predator will limit the growth of the target population (the prey)
- and is sometimes called a predator/prey model. See "The
Refractory Model: The Logistic Curve and the History of Population
Ecology", Kingsland, S., The Quarterly Review of Biology 57, 29-52
(1982). for a good discussion of its history and applications
to population growth problems.

But the logistic equation finds wider use in describing many
situations which become limited by supply of resources (a common
use of the word "logistics"). It has been used successfully to
model such things as the progress of electrification of the USA,
video recorder sales, and many technological advances.

While there are a number of predator-prey relationships at work
in FMD, in this simplified model MAFF/farmers are the predators,
the virus is the prey. Or more specifically, infected farms are the
prey, as data on individual animal infections are not available.
The death rate is caused by culling, movement restrictions and
similar treatments. But culling could be restricted by lack of
manpower for detection and disposal of infected animals, or the
inability to supply enough equipment (like captive-bolt pistols)
for the required levels of culling.

Farmers faced by FMD threats should be interested in seeing that
controls are put in place that bring the population of infected
farms to a limit like the logistic model predicts. The statistics
from the UK foot and mouth epidemic can be tested against these
models to see if this is happening. The results of this could be
useful in monitoring and correcting the strategies being used to
control the epidemic.

The curve labelled Actual is the
Actual Confirmed Daily Cases total (dark blue line), as reported by
the Ministry
of Agriculture Fisheries and Food (MAFF) [now DEFRA] on its web
site. It fits with the Logistic
Fit predicted data (magenta line), suggesting a total of
1580 plus or minus 23 cases would occur (see the left-hand Total
Cases axis, as at 20th May). The brown line is the number of Confirmed Daily Cases (i.e. new cases each
day) plotted against the right hand New Cases axis, and the light
blue line is the Predicted Daily
cases.

The standard error of the estimate (S.E.E.) of actual cases is
just 23 - barely one percent of the predicted final value.

It's clear, however, that beyond 15th May, the logistic fit is
weakening. In fact, from 15th May to around 9th June, a straight
line fit performed better (see Figure 12
below).

The under prediction is discussed
further in 4th May comments at end. At 8th May, it was looking
very reasonable that there might be fewer than 1572 cases, and it's worth asking why was it allowed to go beyond this ?

For comparison, a best Exponential
Fit curve has also been plotted on Figure 1 above, at least
until April 16th after which it goes off the top of the chart (the
exponential curve is also changing by the day). The logistic curve
is clearly a superior model. It will clearly get worse as the
epidemic tails off, and hence will not be maintained for data past
2nd May.

The daily confirmed cases total from the 1967 outbreak has also
been shown 1967 Daily Confirmed Cases
(grey) curve in Figure 1 above (the date
scale for this curve has been left out to avoid clutter). The 1967
curve shows it growing more rapidly and to a higher peak, but also
shows it dying ought more rapidly; it shows now evidence of the
virtually constant daily case rate evident from May 15th
onwards.

It's one thing to come up with a nice looking fit. That's 20/20
hindsight. The big question is how good is the model for prediction
?

One way to look at this is to take a look at what was predicted
at some point back in time. Let's choose the 28th March, so it can
be matched with MAFF predictions. Figure 2 below shows the logistic
fit based on data points to 28th March only (but all points up to
1st May have been plotted).

Figure 2 - Logistic Equation March 28th Model

This predicts a maximum daily cases of 43 on the 27th March -
compared to the maximum of 50 actual daily cases reported by MAFF
for 30th March. The fit for the period data was available looks
good, but beyond 28th March, the fit is much weaker.

Why has the logistic model become a weaker fit ? Is it caused by
a failure in the control effort ?

A reason might be that efforts to control the epidemic did not
scale up to produce the death rate found in the logistic fit at
28th March. That the army was deployed to
assist MAFF about 12th March supports reasoning that suggests the
handling of the epidemic was deficient.

Before concluding that the control efforts weren't effectively
scaled up, let's investigate the logistic curve fit further by
back-tracking to see how well a logistic model might have predicted
the limit as the epidemic unfolded. Figure 3 below shows the
asymptote predicted by logistic fit curves calculated as each day
of data is added.

Figure 3 - Trends of Logistic Limit Prediction

Data from 21st Feb to 28th Feb has not been plotted - you need a
minimum of 3 points to get any meaningful answer (there are three
unknowns), and the prediction for the 24th - 28th February gives a
purely exponential expression (no asymptote, d is zero).

If you were trying to fit a model with more parameters, you'd
need even more data.

The daily growth in the asymptote or Limit of the logistic prediction (red line
above) shows it was not particularly stable, at least until 29th
March. This is in spite of the Standard
Error of the Estimate being very good (blue curve, plotted
against the right hand axis). The total Confirmed Cases at each date is also plotted,
to put the asymptote prediction into context.

For example, at 16th March, the best logistic fit would have
predicted a limit of 392 confirmed cases. But just 4 days later
this prediction was exceeded; in spite of the fit appearing good,
reality showed it wasn't a very useful model. It's interesting to
consider why.

As the epidemic progressed, successive predictions gave an
increasing asymptote, even though both the confirmed case birth
rate b and the death rate d were both decreasing (see Figure 4 below)

The death rate is decreasing more than is the birth rate, so
the asymptote b/d is increasing.

Figure 4 - Beta & Delta Trends

3rd May

Readers who're familiar with the S Howard [HOW0111000] paper will note similarities between
the curve for b and [HOW011000]'s
Figure 4A - which is similar to the basic reproduction number (R0)
in the Imperial College's April 2001 paper relied on by MAFF..

The birth rate decreasing suggests that the spread of infection
is being limited. Perhaps movement restrictions and disinfection
are working, provided we believe that confirmed cases properly
reflect infected animals and not just the rate at which they are
being detected.

But the fall in the death rate of infections suggests that the
infections have become more virulent - they're surviving better.

Is this because, as the scale of the problem increases, disposal
of infected animals is becoming less effective ?

Or does it support the possibility that detection is getting
less effective - so that infected animals live longer ?

One reason infected animals might be living longer is that some
farmers were seeking appeals against neighbour culls in unworthy
cases - thereby delaying the culls. On 6th April, Agriculture
Minister Nick Brown called for more cooperation from farmers in
using the appeals process responsibly.

If detection and treatment of cases is getting less efficient
due to the scale of the epidemic, will it improve as the number of
new cases per day falls off - giving a higher death rate ? Or is
the declining death rate due to some factors not being controlled
at present, perhaps even factors arising at farms considered
properly treated but with some continuing risk ?

A notable difference with this application of regression of a
logistic model and usual textbook cases is that there are several
predator-prey relationships. Primarily, the FMD virus is a predator
that preys on livestock. Farmers are predators that prey on
livestock, mainly for the purpose of marketing their produce. But
in the face of the disease, government and many farmers become
predators that prey on diseased livestock. Some farmers, in their
greed for a fast dollar, have been reported to flout movement
restrictions - thereby assisting the virus to resist its predators.

So attempting to wrap all these relationships into one logistic
equation is a simplification. Whether this is an
over-simplification will be revealed by the goodness of the
outcomes it predicts. It might be expected to work if it's fair to
"average out" all the details.

The benefit of this kind of simplification is that it might help
you understand the overall performance more readily. Sometimes, if
you take a too detailed approach, you can't see the forest for the
trees...

Human predators have a big influence on the birth rate of
infections - with livestock transport most likely being responsible
for this outbreak developing in numerous distinct areas of the UK
(compared to mainly one in the 1967 outbreak, see 1967 comparison paper).

Some influences of human behaviour might be revealed if we take
a closer look now at what the predictions tell about the first
weeks of the outbreak. The initial population size is a parameter
estimated by the regression model, and it suggests that there were
many undetected cases (17) at the time of the official outbreak.
The logistic fit has been plotted in Figure 5 with a logarithmic
vertical axis, to highlight the early period.

Figure 5 - Outbreak Analysis

The logistic fit using data to 12th April has to back-track 3
weeks before the official outbreak date to fall to an average 1
case per day. It suggests that was the real outbreak date was
sometime before 28th January.

Remarkably, the
Independent News reported on 3rd April that Mr David Owen,
Chief Executive of Farmers First PLC, has evidence that antibodies
were found in Welsh sheep exported to France on 31st January - the
same date that the 12th April model suggests should have produced
an average of 1 confirmed case per day (there may have been one
every second day etc.,. before this).

Is there an alternate explanation ? Is this just a chance good
fit ?

Suppose we had been analysing the data available at 4th March.
We'd have noted an outbreak date very close to the official data,
and the standard error of the estimate would also have been very
satisfyingly better. But the passage of time would prove this
estimate and good fit to be poor. Why is this ?

Before losing confidence in the logistic modelling, recall that
it offers evidence of an 8 day lag in control
effect. So the fit before this date is showing the pre-control
characterisitcs

Compared to fits made with another month of data, after 4th
March the "birth rate" (rate at which new potential infectious
sources appeared) halved, but the death rate (rate at which these
potential infectious sources were neutralised) fell by a
quarter.

Entering this less infectious but even less neutralised phase
has the apparent consequence of increasing the total number of
cases by a factor of ten from around 150 (green curve above) to
near to 1400 (magenta curve above). It shows the importance of
looking not just at the sprad (birth rate) of new infections, but
also the rate at which they are killed off.

The adverse increase in total number of cases invites the "what
if" questions. What changed to weaken control so much ? Did the
early efforts to fight the disease in fact cause a more rapid
spread ? It's hard to believe isn't it ?

Next paragraph added 2nd May

Movement restrictions ought to have reduced the birth rate of
infected farms, but should not have effected death rates (unless
perhaps they hampered access by slaughter squads etc.,.).
Otherwise, you'd have expected the death rates to ramp up as the
defence mobilised. The effect on death rates may have been just due
to losing control of the epidemic as it grew in scale, or more
specifically failing to detect and confirm cases accurately in the
first two weeks.

Of course, the prediction of an earlier outbreak could just be
an illusion - a chance fit to the data. But other evidence like
that from David Owen's claims give support to an earlier outbreak
date, that corroborates the model's prediction of an early date.
Later evidence from MAFF also backed up the early outbreak of the
logistic fits.

Next paragraph only, 6th May

The 1967 Comparison cabinet paper
makes it clear now that the outbreak was well advanced by Monday 19
Feb "when a veterinary inspector at an abattoir in Brentwood,
Essex, suspected foot-and-mouth in pigs being held for slaughter".
It reports that infected sheep were "sent to Hexham market on 13
February", which infected other sheep that were then transported
widely across England.

The case taken to Hexham market would have acquired its
infection up to 2 weeks before that date. So the source of it's
infection must have been infected up to 2 further weeks before
that. This evidence was not available when the logistic fit was
done. Hence, a logistic fit that points to an index case in late
January is looked a meaningful fit - not just a chance fit or
simple hindsight.

In a highly dynamic situation at the outbreak of the disease,
where measurement, interventions or control actions take time to
kick in, the model parameters could be changing. The early data
reports might have shown higher growth due to late discovery of
infections (a catch-up effect - it was a growth in discovery, not a
growth in actual cases).

Nevertheless, by 10th April, the asympote predictions had been
quite flat for a week, and the logistic fit was looking a very good
explanation converging on a limit of around 1380 cases.

News stories at this time were claiming a victory, on the basis
of the evidence that new daily cases had been falling for nearly a
week.

Detection Failing ?

14th April

But then came a new burst of cases on 11th to 13th April (see
Figure 1). What was happening ? Was
vigilance falling ? Was the outbreak escalating because of death
rates falling as a consequence of farmers using court appeals and
other action to frustrate neighbour ? See Peter Kindersley's site or
Jonathan Miller's
Sunday Times article of 19th April (was "http://www.whale.to/m/fmd65.html")
for details of the opposition.

Or was it just a pre-Easter flurry of activity ? Given the fall
on 14th, were people inclined to find and report things more
quickly because of the Easter Holidays ?

This paragraph added 2nd May

By 2nd May, it looked like the epidemic was still in decline.
With hindsight, the lull around 7th April might have been the
delayed effect of the 3km cull being introduced some 8 or 9 days
earlier. See later explanation in
analysis of [FERG120401] paper.

But also note the low confirmed cases of 26th April, when
British Prime Minister Tony Blair visited Cumbria (the FMD
hotspot); it's almost impossible to tell if these changes are
random sampling errors, or due to other imponderable factors.

By 13th April, MAFF had posted a warning on its web page that
there were logistical problems with gathering reliable statistics -
all due to the scale the epidemic had reached - the disease
predators were hitting resourcing limits. You might well wonder how
well they can be managing the disease if they can't measure its
progress reliably...

Others were not so kind:

'My correspondents saw Brown’s claim that everything was
under control as just another pathetic Maff lie; and after Blair
delayed the general election and took personal command they noticed
that nothing changed.

Soldiers moved in to the culling fields, to be appalled at
Maff’s incompetence. Every day at a Whitehall command centre,
a mole revealed to me, top civil servants met to plan their
campaign against foot and mouth. The meeting was conducted standing
up, supervised by a brigadier.

This was the "show and tell", where Maff was forced to fess up
to its daily disasters (eg slaughtered animals polluting water
supplies) as officials from other agencies bit their tongues in
disbelief.

Difficulties in detection and accurate reporting may well be
undermining the accuracy of the logistic fit, and preventing it
homing in on the parameters of the underlying disease processes.
Detection failures could explain the apparent fall in the death
rate (it's hard to kill what you haven't detected).

Undetected cases may be allowing the infection to spread more
extensively, and would make it difficult to predict the ultimate
limit to the epidemic. No longer is the incremental death rate
varying in proportion to the square of the size of the population,
as assumed in the logistic equations; it may be a less simple
function, like a smaller power of the population size e.g.
proportional to P1.5,
P1.2 etc.,. (another
degree of freedom to the model !).

As an exercise, models can be estimated with the population's
exponent for the incremental death's as a parameter. For data at
14th April, it producesinstead of , giving a higher limit around
1560 instead of 1420. The standard error of estimate is lower than
the simple logistic model. But a quick check of previous days and
weeks will show the model parameters are even less stable, change
day by day also, and the death rate P exponent gets closer to the
standard logistic curve's 2 as fewer recent points are included in
the data. A P exponent of 1 is pure exponential growth - so getting
results less than 2 isn't what you'd like.

Ultimately, farmers would like the FMD epidemic to reach a
limit - to behave like the logistic equation assumes. While new
cases may be spread in proportion to the total number of infection
cases, the elimination must grow in proportion to the square of the
number of infection cases to neutralize the growth. To achieve
this, infections have to be reliably and speedily identified, and
followed up with prompt elimination.

The task force working on detection would need to grow
in proportion to the number of confirmed cases, as would the
training and deployment of slaughtermen - a very
challenging logistical exercise. Managing access restrictions and
cleanup of infected properties would be even more daunting.

Next 3 paragraphs added 16th April

In the week to 1st April, the numbers needing to be culled
would have to be double that of the previous week.MAFF
have had difficulty reporting cull rates. By 14th April, it
reported that the average daily slaughter was 19,000, 31,000 and
34,000 for the three weeks ending 1st April. There wasn't even a
10% increase where 100% was needed, and disposal rates were even
more dismal.

Unless they've become unusually good at targetting just the
infected animals, they haven't got it under control.

This might be happening fortuitously if, under stress, the
slaughter squads are still reaching the critical region - argued by
some to be within 1 to 1.5 km of the index case ( see Peter Allen's
comments). The weakening in the logistic fit, though, suggests
they aren't quite getting there.

Is it any wonder ? Without more reliable feedback of cull
numbers, isn't the challenge of directing an effective campaign
being left more to good luck than to good management ?

The logistic model highlights that to control the extent of the
outbreak (the limit to the confirmed cases population), you need to
control two factors: reduce the rate of infection spreading (birth
rate of new cases), and increase the rate at which infected sources
are eliminated (the death rate). The elimination of infection
sources (animals and farms from which they come) must be achieved
at least in proportion to the total confirmed cases.

Variations evident in the Logistic model regression analysis,
particularly the declining death rate, suggests control of the FMD
spread had been less than ideal up until 18th April in the UK.
MAFF's inability to monitor the progess of its slaughter squads
does not augur well for an early end to the epidemic. Strenuous
opposition to the culling of apparently healthy animals may have
made things worse. See later discussion of the vaccination debate that rages over the Easter
Weekend (circa 13th April)

Some proponents of vaccination are responding to perceptions of
failure of the culling policy, especially in relation to safe
disposal of carcasses and public acceptance. The declining daily
cases suggest the policy is not an abject failure.

Other experts argue with the details of the culling policy,
arguing that it is wasting resources by being poorly targetted. The
recent weakness of the logistic fit supports suggestions that the
cull is not being handled most efficiently - and poor targetting
could be part of the reason.

But to decide that, you'd need much more data than has presently
been made available, and perhaps more than what anyone has reliably
compiled.

An academic analysis of the outbreak, up to 29 March 2001, can
be found in the paper by Ferguson et al [FERG120401]

Results from this research group featured prominently in the
Chief Scientists's analysis, and MAFF press releases in late March,
April and May.

[FERG120401] presents a highly
detailed mathematical model which some readers will find
mind-boggling or obtuse. It aggregates the diseased population of
animals into units of farms (herds) in up to 5 states of infection.
It then models how disease might spread from farm to farm under
various control scenarios, represents at least 9 parameters of the
disease transmission process and makes a large number of
assumptions and simplifications.

Despite this impressive effort at precision, there was one
parameter, rI, that could not be estimated from the
available data. This parameter related to the change in infectivity
that might occur at the time a farm reached reported status. It was
dealt with in the paper by discussing the sensitivity of outcomes
to it.

Some experts claimed the model needed even more
complexity. For example, that the rates of spread of infection were
significantly different in the three main species (pig, cattle and
sheep). And that there were several distinct epidemics occurring
that should be modelled independently.

But the inability to estimate rI suggests there might
not have been enough data to get any more meaning from adding
further complexity. You could be forgiven for thinking they'd
already stretched the data a bit too far.

The lowest curve of [FERG120401]Figure 4A,
for rI = 5, and mean time to slaughter of 12 hours,
might contradict this; but that case seems to also indicate that
becoming reported makes the farm 5 times more infectious and leaves
you to wonder whether the cure that reporting invokes is worse than
the disease.

Did [FERG120401] really mean to say 5
times less infectious ( for example, because all the
infection spread occurred before you could detect it ?).

Also, reduction of the mean time to slaughter to 12 hours (post
31st March) doesn't fit the reports of delays increasing in
slaughter and disposal times.

Figure 6 - Ferguson's March 28th Model

On the evidence to April 20th, [FERG120401]'s March 28th Best Fit model appears
to drastically overestimate the incidence of confirmed cases (by
almost 3 times). In contrast, a logistic curve fit on data to 28th
March predicts a maximum daily cases of 43 on the 27th March (see
Figure 2 above ) - much closer to the
maximum of 50 which occurred on the 28th March.

The logistic model of 28th March under-estimates the asymptote,
as is clear from Figure 2, and Figure 3.
This is likely to be evidence that subsequent to 28th March,
controls were not applied in a precise logistic fashion (death rate
not proportional to square of confirmed cases). But it is
nonetheless a much better fit than the [FERG120401] fit at the same point in time.

Did all the complexity in [FERG120401]'s model achieve something useful, or
does it just get in the way ? It has lots to say about altered
control scenarios, that may need a complex model to explain, but if
the model doesn't predict what happened, how meaningful is it ?
Does a model explain anything if it can't predict ?

At the better resolution available in Figure 7, some revisions
in the previously published confirmed daily cases data can be
discerned. Figure 7 has plotted a point near 24th March with about
60 new confirmed cases ([FERG120401]'s ( if you look really hard,
Figure 3A also has a point with 60 confirmed cases, around 24th
March). This point disagrees with the MAFF daily
situation report graph dated 19th April, that shows a max of 50
and figures near 45 around 24th March.

Data for [KING200401] curves has been scaled off Figure 7, and
due to the coarse scales used in Figure 7
isn't brilliant quality (promise: send me the source data files,
and I'll update this within 48 hours). And nobody has checked it,
but lil' ol' me (and maybe now you !). But it is good enough to
indicate some major anomalies (green highlighted points).

Is MAFF or Ferguson right ?

If anyone from MAFF, the Imperial College, or Prof King's corner
is able to verify which data is correct, or offers any explanation
for it by
email to me
, I'll publish it here within 48 hours.

Within hours of publishing this, Andrea Jones
sent me a link to her graphs, http://www.hjones-sons.co.uk/graph.htm
which she compiled day-by-day from MAFF's web page. The confirmed
cases data looks different again (although it doesn't quite make
Ferguson's peak of 60).

Reality Check#2: there were 3
confirmed cases on 29th April. Logistic prediction of 4 takes the
money from the Ferguson prediction of 21.

Ferguson's data is truncated at 29th April, and in any case the
relaxing of the cull undoubtedly changes the parameters depicted in
his 17th April model. So we can't get any more predictions from his
data. At the end of the experiment, logistic model wins 2-0, a
victory for simplicity.

From Figure 8 data, [KING200401]'s confirmed
cases can be compared against it's Ferguson model fit (orange line
from Figure 7) using the Square Root of the Average Squared
Deviations a.k.a. Standard Error of the Estimate (S.E.E.) as a
figure of merit.

S.E.E. was 8.2. Between MAFF's confirmed cases and Ferguson's
model, S.E.E. was 7.77. Hmm. Did the model have better data than is
shown in [KING200401] ? Or is it time to think GIGO : Garbage In -
Garbage Out ?

Now compare MAFF's confirmed cases and the logistic model - the
S.E.E. is 5.88. On this criteria, it is a noticeably better fit;
the SEE for Ferguson's model is 30% higher (and I could do better
with another parameter for the death rate P exponent). Doesn't your
eye confirm it too ?

Next paragraph inserted 28th April

By 27th April, the logisitic curve SEE was 6.08, and Ferguson's
model was 8.2 some 34% higher.

Given the huge change in the peak confirmed cases compared to Figure 6, it's reasonable to ask what was
changed after 28th March ? Has it now got a better rI
estimate that's very different to the value of 1 assumed in Figure
6 ?

[FERG120401] discusses culling
strategies based on distances from index cases (see especially
figure 4B and 4D of the paper). The new model is hard to reconcile
with this, referring to "neighbour" culling. Whatever that means
isn't precisely clear but maybe it is not the same thing.

Notice the downward bump in the model just after the 29th March
? Was it the kicking-in of the 3 km cull started in Northern
Cumbria (some uncertainties: neighbour cull announced 25th March, 3
km cull in NC on 30th March, how many days before it really
happened, did they try to model that, more parameters stetching the
data even thinner etc.,. ) ? Or maybe the germs got a little tired after maxxing
out ?

Seriously, there's also a subtle kink in Ferguson's model fit
around 4th March. Was there a discontinuity in the model at this
time (for example due to some new strategy brought into play) ? The
4th March was identified in Figure 5 above
as one where something interesting may have happened. What was it
?

This sub-section added 29th April, 2001

As noted earlier in discussing Figure 3, it appears to take 8 or
9 days for a change in controls to be reflected in the confirmed
cases counts.

The movement restrictions were introduced about 23rd February.
It may have taken until 4th March for their effect to bight.

[FERG120401] states that there were
changes in R0 due to the movement restrictions, but does not
identify the date at which this change was applied in the model. So
maybe that explains the 4th March kink.

Now what about the 29th March dips ? One
possibility has been suggested by James Annan: that this is the date the
ring cull kicked in, and the dips are the effect of the ring cull
introduction. The ring cull might have produced a step fall in the
count of confirmed cases, by taking culled farms out of the count
that were infected and otherwise on the path to confirmation.

In turn this fall in confirmed cases would reduce the number of
culled farms, particularly neighbour culls. This might lead to a
subsequent increase in infections some days later - giving a
"bounce" back effect - and perhaps setting up an oscillation in the
spread of infection (if not critically damped, as in the design of
car shock absorbers etc.,.)

But [FERG120401] does not discuss why
a culling step change should be evident only with the most extreme
rI cases, and not for all the cases depicted in
Ferguson's Figure 4A.

Ring culling was announced around 23rd February, only 6 days
before.

And if you look at the real data around 29th March in Figure 1 - there does not appear to be any
significant dip (the next sustained dip after then is 10th April).
Nice explanation, but doesn't match reality too well ?

Let's hope all the details get published soon. It would be even
more convincing to see another researcher replicate the Imperial
College's results. In the meantime, does it look any better a
prediction than the simpler logistic model ? Which model predicts
next week's outcomes better ?

When it comes to forecasting the daily confirmed cases, the
score is 2-0 to the logistic
equation.

The logistic model can't say much about how to fine tune policy
details to work best in the future. It can look back and say that
you've not done as well as is desirable (see the gap between the 28th March model and latest data), and
understanding its good fit compared to complex models can give some
insights into broad guidelines.

Potentially, the more complex models could say something more
about policy detail alternatives. But whatever they predict has to
be seriously discounted by their proven poor prediction record.
Isn't the proof of a scientific theory what it can tell you about
the future ? At best, the complex model is giving the relative
merit of the options; at worst, you should wonder whether the data
and parameters have been so messed up that even the ranking of the
options is not credible.

A quasi-logistic model, with an
additional parameter for the exponent of the death rate term in the
differential equation, can predict somewhat better than the pure
logistic equation - but perhaps only because the control efforts
have been relaxed once the peak was passed.

Maybe it's better to KISS, and to pursue the epidemic with full
vigour during its decline.

Victory Claimed ?

Professor King has been quoted (BBC News 20th April) as claiming
the outbreak was fully under control, on the basis of the down
trend in daily new cases. Brave predictions on the basis of
questionable data ? Will these words come back to haunt him ?

Maybe Ferguson's model has gotten way better, and maybe he really
does have the best quality data. But it might be prudent to
prove this by checking it's forecast for next week against reality
before you get to thinking it's all under control. It
might also be prudent to consider whether the trend in the fit of
the logistic model might indicate that control has been less than
optimal.

There have been reports of census collectors breaching infection
control guidelines. Goodness knows how many improperly trained
tourists might have also flouted the rules over the Easter Break -
it wouldn't surprise to see an escalation over the two week after
Easter as this and other relaxations in the controls emerge
([FERG120401]'s model seemed to lack a parameter for people's
stupidity, the logistic model aggregates everything like this into
it's death rate parameter).

As for the future management of the outbreak, the vital question
remains: What is the least risk strategy: changing policy or
refinement of the cull policy ? Are the data and models reliable
enough forecasters to be useful in deciding this ?

Or does it take too much time to decide this rigorously - so
much that the show will be over before the answer comes to hand,
with properly checked data and peer-reviewed scientific facts ? And
even if you could get a certain answer, can you gain sufficient
public support for a change for it to succeed ? Then think about
what MAFF's liabilities might be if culling has been over-zealous
?

There might still be squillions for the lawyers to make out of
it, once the epidemic is put to bed.

Next two paragraphs inserted 27th April

On 26th April, the Minister Nick Brown (see http://www.maff.gov.uk/animalh/diseases/fmd/news/minister.asp)
announced to Parliament a relaxing of the cull strategy. Thereby saving Phoenix, a calf that was
found near its slaughtered mother in Devon, and who's owners had
taken MAFF to court to prevent it's culling (see BBC
news ). See the UKBA archive (thread subject Phoenix) to review
the debate - not everyone believed the calf survived
unassisted.

By 27th April, MAFF was relaxing the movement restrictions in
"provisionally free areas". Is it premature ?

<28th April

Just relaxing the cull will tend to produce a stepwise increase
in the number of confirmed cases - because you will now be
counting-in cases that were in the process of being confirmed (that
were previously culled before confirmation due to the neighbour's
property being culled). You will also, in some cases, be failing to
eliminate incubating infections, or ones that haven't been detected
that are capable of infecting other animals and farms. The poorer
logistic fit from the 24th April may be reflecting this.

Even though the fit is weakening, the logistic equation has
proven to be a better predictor of the confirmed cases than the
much more complex [FERG120401] and [KING200401] models relied upon by MAFF in
defending it's strategy.

Phoenix Rising ?

3rd May

It's interesting to see Andrew Heggie's animated graph (1200 Kbytes, no
delay, or 760 KBytes, 0.5 sec per
frame) of the spread of the epidemic. Up until day 10, the
outbreaks were scattered fairly widely. But then a clear
concentration developed around Cumbria, and to a lesser extent in
two other areas.

What went wrong in those first 10 days at Cumbria that let
things get so out of control ? Even as we should be reaching the
end of the epidemic, Cumbria is still the hotspot. Are these things
still going wrong ?

The rise in cases in Cumbria on 2nd May, and weaker fit of the
logistic curve in the last few days, suggests that things may not
be under control. The relaxing of the cull occurred 7 days ago, and
evidence to date indicates such changes are taking around 8 days to
show up in the confirmed cases. The next two days should tell the
story - if MAFF don't come clean today (based on their
kept-to-themselves infection reports) and admit things are going
poorly again.

Of course, MAFF may be feeling comfortable as they are still
ahead of Ferguson's predictions, and, as they have highlighted, the
the UK 1967 epidemic had a "long tail". Such a long tail did not
feature in Ferguson's Figure 3D. It
indicates a lack of aggression against the disease once it
wanes.

Do you accept this because it happened
before, or do you evaluate the more aggressive option ?

Ferguson's recent long-tailed predictions may be a self-fulfilling prophecy that could be more
costly than an unrelenting pursuit. Or they might be a clever way
to argue to a court that they'd done better than the expert's
predicted, and hence have been duly diligent.

4th May

For 3rd May data fit, the estimated asymptote is less than the
actual number of confirmed cases (1538 v 1543). While well within
the SEE, it is nonetheless indicative of a weakening fit. A fit of
points from the 10th April gives an SEE of 3.1 and a prediction of
1613 cases. A fit from the 20th April gives an SEE of 2.8 and a
prediction of 1628. These trends indicate that the control has been
less than unrelenting.

"The battle against foot-and-mouth is nearly over, Tony Blair is
set to announce on Thursday. The prime minister's confident
assessment, in his first formal press conference on the crisis, is
expected to pave the way for a general election on 7 June. "

The Prime Minister's actual statement
later that day made no such claim, and warned "... it is not
over yet. We cannot in any way be complacent and it is essential we
remain fully vigilant." The BBC's perceptions are different to
the government's, and may be sending an unhelpful message that
encourages complacency.

MAFF statistics for 3rd May show a new case was confirmed in
Somerset, an area previously declared disease free. This is fairly
direct evidence that the declarations of disease free status were
premature, and that full vigilance had not been sustained. This
corroborates the conclusions suggested by the logistic fits that
there has been a slackening in the effort.

Further suggestion of complaceny are the allegations that one
milker, whose own farm is now a confirmed case, had visited 15
farms in the previous fortnight and had attended a MAFF vaccination
lecture, declaring that he'd not visited any farms and showing a
rank disregard for the risks he created. (see The story of Mr
Norman, in The
Independent, 7th May)

5th May

In view of the slackening of the logistic fit, it's worth
showing the better fit obtained where the death rate exponent is
estimated (rather than 2). This gives a quasi-logistic fit as shown
below, with an asymptote of approximately 1600, and a Standard
Error of Estimate of 8.5 (half the pure logistic fit). Decreasing
the exponent tends to bring some asymmetry in the tail of the daily
confirmed cases that better matches the reality of declining
vigilance.

King, at the same conference, re-used Ferguson's graph
(looks like Figure 7, updated with more
actual data points). King said "... we have to be a little
worried about prediction when we get down to very small numbers of
cases." It may be hard to tell the difference between dodgy
data reporting and random errors.

The Figure 10 fit makes the last few days data look a little
less like a resurgent outbreak but at no other time in the outbreak
have we had six days go by without a decrease in daily confirmed
cases.

6th May

May 5th saw a downturn and 6th brought a further decline.

May 6th also had MAFF revise it's confirmed case data for May
5th, down by one, and include a note on their site - thereby
proving the Minister's 3rd May assertions correct even if the movement was in
an opposite direction to what the allegations had claimed (a
confirmed case became dangerous contact, not vice-versa)

Stay tuned to see if the epidemic will rise from the
ashes...

By June 15th, FMD had not fully risen from
the ashes, but with daily new cases showing no decline, it was far
from eradicated.

9th May

By 9th May, there had been 3 successive falls in daily cases,
bringing a convincing match with the logistic model. If another
outbreak occurs, it will in all likelihood be much better
controlled, and will produce a different logistic equation -
needing perhaps a bi-logistic model to describe the pattern; that's
a way more complex story which hopefully can be avoided by
maintaining the effort for a significant time after the last
confirmed case.

Five cases in each of the last two days continue to show that
the fight is loosing intensity - even at a time when resourcing the
fight ought be much easier.

If you compare the latest logistical fit in Figure 1 with the 28th March prediction in Figure 2, there have been over 200 more cases than
might have been expected with a more vigorous fight against
FMD.

Possible reasons for a less than vigorous fight were put forward
by Brigadier Alex Birtwistle, the Army officer who spearheaded the
fight against foot-and-mouth in Cumbria, and retired from the army
at the end of April. He said,

"People are still transiting sheep illegally
and there's strong anecdotal evidence to suggest that is the
case.

"Either to infect them so they can claim compensation, or
simply to keep sheep they haven't previously declared one step
ahead of the cull process. "

A rise to 8 confirmed cases - Phoenix mightn't be rising from
the ashes, but the battle against FMD is clearly not progressing as
well as it could be.

News from MAFF on 11th May that some 30% of blood tests of
confirmed cases proved negative, and only 18.4% of neighbour culls
proved positive, will help those resisting culling and may well
bring further setbacks. MAFF claims, however, that it is not
conclusive evidence that the animals were not infected. Taking it
as evidence to stop culling could bring further setbacks.

13th May

An alternate explanation of why MAFF's predictions are higher
than actualities:

Perhaps, MAFF's predictions were high because Ferguson assumed
24 hour culling after the confirmation of a case. But in fact, 3 km
neighbour culling may have caused many herds to be culled very
close to the time when they became capable of transmitting the
disease. More aggressive culling reduces the epidemic's
magnitude.

If every herd was culled on the day it could spread infection,
you would have an ideal logistic fit. The deviations we see above
the logistic curve might be a measure that MAFF's policy changed in
time and didn't quite get to this ideal logistic fit.

It is another question altogether, though, to decide whether the
cost of this level of aggression is warranted. Whether vaccination
can approach the aggression needed for an ideal logistic fit is
also another question. Both these decisions might change if the
outbreak is not treated quickly and the numbers to be
culled/vaccinated become large.

16th May

The high number of confirmed cases for the last few days
indicates the fight against FMD has lost it's sting. The logistic
fit is weakening considerably (with the projected limit 1572 now
exceeded by more than the standard error of estimate 21 -giving
total 1593 v's actual of 1600). This may be an indicator that
infected herds are not being discovered and culled quickly
enough.

19th May

A "false dawn" of 0 cases on 17th May has been followed by
several days of high cases. The last two with 4 days each confirm
that the outbreak is not being eliminated at a satisfactory rate.
Perhaps a closer look at the geographic spread of recent cases
might indicate whether the neighbour cull is losing its effect, or
whether these cases are arising due to laxity in the
transport/infection controls.

Unless some improvement is made over what has happened in the
last week, this outbreak could drag on indefinitely...

23rd May

With confirmed cases rising to 8 on 23rd, it's become clear that
another outbreak has been unleashed, centered on North Yorkshire.
MAFF had to send 25 vets into the area, some coming from as far
afield as Australia (according to BBC reports).

So who pulled the vets out too soon ? Farmers in the Settle
(North Yorkshire) were feeling so abandoned that the Minister and
an army General had to scurry into the area on 22nd May to show the
locals hadn't been abandaned.

But the statistics show very clearly there has been a failure to
pursue FMD relentlessly - the lid wasn't nailed on the FMD coffin.
It was let out again to wreak havoc around North Yorkshire, and a
mini-remobilisation has been needed.

26th May

Minister Brown was forced to deny allegations that MAFF had been
manipulating FMD statistics to bolster the governments fortunes
during the election campaign. Let's back incompetence ahead of
conspiracy and continue to treat the statistics as correct.

We have to then conclude the disease is not under competent
control. Since 6th May, there has been an average of 4.1 cases per
day, and there is no discernible decline.
The number of cases is growing in a straight line (see Figure 11). FMD is not being controlled adequately.
It would not take much denial based behaviour see a return to
exponential or logistic growth rather than the decline so
needed.

There has been linear growth in total cases since around 4th May
- approximately 8 days after the 26th April movement restriction
relaxation. The growth appears to be occurring in "pockets" of
North Yorkshire and Lancashire. A conjecture might be that multiple
disconnected outbreaks sum up to such a linear growth.

While MAFF is making defensive claims that these outbreaks came
from long-dormant infections, it has also pointed the finger toward
farmers movements. So shouldn't you ask: were the relaxation to
movement restrictions too early ?

There is also a evidence from Peter Alan that the Chief Vet's
definition of "contiguous" is now also more relaxed. Too soon also,
unless you like to think that the present rate of disease and
culling is reasonable.

At the present rate, MAFF and it's slaughtermen have got a job
for life that's probably paying them better than their old job.
Don't expect it to end until someone realises how dumb it is to let
this continue.

3rd June

Thirteen new cases show growth is tending towards a renewed
outbreak. It's time to look for evidence of a new logistic process
- which appears to take-over from the initial outbreak from some
time around 15th May.

On the data from 15th May to 2nd June, however, the best fit is
now a straight line, with 4.39 cases occurring per day on average.
The only good news in this, is that it's not an exponential growth
-Yet. The bad news is that it's equally
clear that it's not a controlled logistic growth - there's no death
rate, no asymptote = no end in sight.

Figure 11 - Total Cases Since 15th May to 2nd June

Last Wednesday, the BBC had reported

"Prime Minister Tony Blair has said that new
clusters of foot-and-mouth disease had been "expected" by
government scientists."

Yet none of their previously published graphs predicts a
resurgence like we are now witnessing. None predicted that there
would be a straight line upward trend over any two week period.
Probably would have been shot down in flames if they had. Any such
prediction would have made arguments for vaccination look
overwhelmingly good at this time.

Blair's excuse that the "scientist expected" new clusters is
very poor. This site did not make any such ridiculous suggestion
that this was scientifically necessary or predictable. Such a
resurgence should not have been expected and it's occurrence is a
sign of failure. If the fight had really been unrelenting there'd
be no more cases occurring by now. (see Figure
2 for 28th March prediction).

5th June

The straight-line fit is now weakening (in terms of least-square
error), and it's slope is rising to 4.6 cases per day. It's still
better (in lse terms) than either the logistic or exponential fit,
but is indicative that the outbreak is accelerating upwards. Fears
that the awful truth will only emerge after the election are
well-founded. They've only got to hide it two more days...

6th June

Two more cases, together with a new inclusion of 4 previously
confirmed cases from Northern Ireland in the total. Don't believe
it, until the election is over. MAFF has responded to rumours of
preparations for a Mass Cull with a carefully worded rebuttal http://www.maff.gov.uk/inf/newsrel/2001/010604b.htm
(their link posted on 6th June was broken, this one is right !). It
concludes with a guarded (I've left their spelling errors
verbatim):

The Ministry, together with the Army, are still
engaged in a complex operation in many areas of the country,
particularly in the Settle/Clitheroe area where there are a serious
number of cases. It is likely to be some time before the outbreak
is finally dealt with; a great deal of work still needs to be done
on the ground and logistical planning to support this effort goes
on, involving a wide range of services.

Any planning that is being done is specifically to address the
current situation and as a contigency for any new outbreaks. It
does not indicate any plans for fundamental changes in the culling
regime.

7th June

Britons set off to re-elect Blair comforted by another low-case
day - just 2 more cases. The only thing there should be doubt about
is how long it will take for the unpalatable truth to emerge in the
statistics.

In the meantime, you can amuse yourself by trying Ian Clark and
Adrian Smith's epidemic simulator
to investigate how fairly complex behaviour can emerge from a
relatively simple model of epidemics. With 5 parameters, it's more
complex, of course, than the logistic model - but falls short of
the Ferguson/Howard style of models which have over 9.

10th June

Within days of the election passing, MAFF's counts have risen,
to maintain the average at over 4 cases per day. Further
relaxations in opening of footpaths etc.,. have occurred. No end is
in sight.

Media reports of worst case predictions suggest FMD could
continue through to early next year. This was a response to
worrying outbreaks in unexpected areas, which were relatively
remote from previous infections. Experts warned these indicated FMD
was going to have a "long tail".

It would be a real step forward if the statistics showed any
kind of tail - even a long one. Instead, the daily average cases
since 8th May has been increasing from an average 4.3 cases per day
up towards 4.8. No impression is being made on an apparently
persistent level of infection. How long before it's right to say
its become endemic, not eradicated ?

Figure 12 - Total Cases since 15th May

16th June

The straight line fit from 15th May indicates a trend of 4.9
cases per day, even though the last few days has brought only 4 per
day (see Figure 12 above) The logistic fit since 15th May is now
producing an appreciably better fit (including a lower standard
error of estimate). However, the logistic fit looks decidely poorer
over the most recent week, and is obviously underestimating. A
wishful thinker might take the better logistic fit as slight
evidence of some attenuation in the outbreak. Or it might be
someone still fiddling with the statistics.

In particular, MAFF have advanced the daily "cut-off" time from
19:00 to 17:00 on 15th June. Although they promised to publish the
equivalent 19:00 figures "side-by-side", this did not happen on the
15th.

17th June

Curiously, we have now had 5 days running with exactly the same
number of daily cases (4). Theoretically, such "runs" can occur
amidst a randomly sampled process. But it does seem a little odd
this has only happened in this poorly controlled phase of the
epidemic

18th June

The BBC's Alex Kirby has described FMD as the
Disease that Refuses to Die. . To see how poorly things are
going, this is now day 116 of the outbreak. At this stage in the
1967 epidemic, as the light grey curve in Figure
1 shows, things were decidedly better - it was virtually over
at that time in 1967. You won't hear anymore claims that this has
been dealt with as well as 1967...

So why is the eradication going so much worse now ? The 1967
comparison paper makes much of the increased livestock movements
that now occur, which led to FMD spreading more extensively this
time. If that's the case, is the answer as simple as preventing
such extensive livestock movement from occurring - i.e. turn the
clock back to 1967 farming practices ?

On 9th June, MAFF became part of a new department - with a new
minister and a new name which lacked any reference to agriculture,
viz Department of Environment, Food and Rural Affairs (DEFRA). The
new minister, Margaret Beckett, swung into action on 14th June and
has promised a culture of openness and cooperation ( see Beckett
extends hand to farmers) . Will this be enough to allay the
concerns of those who wonder why the word Agriculture has been
dropped from the departments' title ?

Can the new minister rectify the shortcomings, and make up for
the ground lost between early May and now ? If secrecy and a lack
of cooperation have been the problems, will the minister's words
about openness and cooperation be enough to set things right ? Have
the bureuacrats been trembling at the knees and lying awake at
night after hearing the Minister's words ? Will we see any visible
signs of a change in their secrecy - for example, can we expect to
see more detailed and transparent statistics (e.g. daily suspected
cases) published on DEPRA/MAFF's site ?

Don't hold your breath waiting for it ! As of 21st June, the
total cases trend line continued to rise linearly, and look the
best fit for the data...

25th June

Just one case on the 24th will have optimist's and wishful
thinkers believing the down-turn indicated by the logistic fit from
15th May is happening. DEPRA is certainly behaving very
optimistically, if not bravely. From 22 June, livestock from within
Infected Areas will be permitted to move, under licence, for
slaughter in abattoirs outside an Infected Area (but not in
Provisionally Free Areas) for human consumption.

Additionally, the Minister promised to open more pathways etc.,.
- yet still went on to admit it's not all over yet. "She said it
was hugely important that no one relaxed their guard" (see BBC
report
Further farm restrictions lifted ).

Why is everyone behaving like it's over, when there is scant
evidence of any decrease in the outbreak ? The Minister has
promised an inquiry - let's hope these latest relaxations are
included in its scrutiny.

28th June

The last three days have shown a fall in the daily cases. The
last few points now lie almost half-way between the straight-line
fit (from 15th May) and the logistic fit - see Figure 12. It's an encouraging decline.

1st July

A day with no new cases hints that the end may be close. But
it's only 8 days since the policy changes of 22nd June, and may be
sensible to wait a few more days before believing this too
strongly.

6th July

There now seems to have been a decline in the daily case rate -
perhaps now to 3 per day from the previous 4.8 per day. But the
disease won't go away. On 4th July, DEFRA announced
that a video would be sent to 90,000 farmers in England to
reinforce the need for bio-security. Professor King said the
measures were needed as many farmers had been relaxing their guard.
King said "Biosecurity measures are being
relaxed. If they had been observed, I have no doubt the disease
would be at a much lower level by now".

NFF president Ben Gill was reported as agreeing, but claimed a
similar relaxation occurred in 1967. As the graphs in Figure 1
shows, if the 1967 performance were matched, there'd have been no
new cases since 19th June; the relaxation is much worse in this
outbreak, and it is at least 5 weeks behind the 1967 situation.

It's good to see actions from DEFRA, but unfortunate to hear
farmers leaders making misleading comparisons with 1967.

10th July

The logistic fit since 15th May, although better in least square
error terms, is looking shaky (see Figure
12)- the recent high case rates (mainly in Cumbria and North
Yorkshire) look a better fit to the straight line fit - with an
average daily case rate of 4.4. There has been almost negligible
decline in case rates since 15th May. Let's hope that things
improve when the "video-effect" kicks-in in after 12th July...

12th July

Looking back at the evidence from Figure
1, it's clear that shortly after relaxation of the 3 km cull
(26th April), the outbreak's control switched from a good logistic
decline to this constant daily case rate mode. Doesn't that suggest
something strongly:if you want to eliminate foot and
mouth disease, reinstate the full pre-emptive 3 km
cull. It's a real gamble waiting to see if other
tricks, like video campaigns, will be as effective as the 3 km cull
clearly was.

14th July

Although the logistic fit from 15th May to 5th July looks good,
from 5th July onwards the decline it indicates clearly is not
achieved. Once again, the outbreak escalates. A linear fit from 5th
July with 3.86 cases per day looks an excellent fit from 5th to
12th July (such a good fit that its hard to discern from the actual
cases in Figure 12 above - so I plotted the line back before 5th
July to help you see it). Curiously, DEPRA is claiming the weekly
average case rate has been 3 for the last two weeks when in fact
it's closer to 4 - just wish they could truncate the outbreak as
well as they can truncate their stats, don't you ?

18th July

A few days now with high cases and a frightening 10 cases for
the 18th, have "raised" the straight line fits, That from 15th May
is now 4.3 cases per day, and from 5th July is 3.8 cases per day.
There's now been plenty of time to see the effect of the "video"
campaign - it's been clearly
ineffectual.

Certainly looks never ending, doesn't it ? Farmers are getting
"toey" about their inability to sell their "light lambs".
Maybe they'll just have to get used to that - cause
everybody's doing too little to eradicate this
disease.

The logistic fit from 5th May to 23rd July has an SEE of 9.12,
compared to 9.4 for a straight-line best fit to the same data. It's
pointless continuing with modelling the process as logisitic over
this period of time. So now Figure 12 show the logistic fit
truncated to 5th July - a point where there appears to be a clear
breakpoint in the trend. Similarly, the straight line is broken
into the second line (and now coloured red also) at 5th July.

Unfortunately, from 5th July there is very clearly an
unattenuated growth averaging 3.86 cases per day. This bumbling can
only fuel the fires of those who'd argued in favour of vaccination;
culling, as now practiced, is clearly producing no end.

23rd July

Lord Whitty, the new DEFRA minister, has announced reinforcements of
the bio-security measures in the North Yorkshire area - in the
face of the unabated progress of the disease and fears of the
outbreak getting too close to very large pig herds in North
Yorkshire. The alarm bell was ringing on these fears for over a
week before DEFRA responded. The outbreak is still averaging 3.85
cases per day since 5th July.

If you are looking for more information on the nature of FMD and
issues debated during its course in the UK 2001 outbreak, Sarah Wroot's
UKBA FMD FAQ is a well-researched compendium of information
compiled by educated community activists from the
uk.business.agriculture usenet group. It was published in June
2001, and hence post-dates some of the discussions above.

Cases back to 4 today, after two low days of 1 and 2. The cull
of hill flocks in the Brecon Beacons (Wales) has created some
alarm, having been based on serological testing - much more of
which is now under way. A long held fear that FMD has gotten loose
in these flocks is looming larger. There appears to be suspicion
that undetected FMD is at large in sheep flocks, and perhaps is
providing a pool of infection that is continuing this outbreak.
Serological testing and culling is seen as an evil necessary to mop
up these infection sources.

DEFRA has announced further intensification of the biosecurity
measures around the Thirsk area of North Yorkshire. DEFRA's
capacity to announce such changes appears unmatched by its ability
to implement them, as farmers are still left uncertain as to how
the measures announced a week ago are to be applied.

DEFRA also announced (30th July) an immediate change to the
valuation of culled livestock. Stock would now be valued
individually, not at a flat rate as had applied since the early
weeks of the outbreak.

1st August

Raising again allegations made long
ago in May, Nuala Preston, a Pembrokeshire, West Wales farmer, has
claimed she was offered an infected sheep carcass for £2,000
- (
BBC news 30/7 ). This time, DEFRA and the Powys police are
investigating (30/7/01). Each slaughtered sheep was fetching
£90 - said to be well above their market value.

Nobody has produced an epidemiological model that results in the
obvious straight line trend we now see. One way you might get such
a constant flow of cases is if there is an individual making a
deliberate effort to infect farms, who can't get to more than 4
farms a day. Such an individual might also cause the kind of
non-contiguous infection outbreaks now being seen (in areas not
previously near infected sources).

Nuala was horrified by the offer, and it really beggars belief
that so many farmers could be party to such a crime. Fortunately,
DEFRA has now changed to a model requiring valuation of the culled
stock for each case, and perhaps this might bring some uncertainty
and restraint to the process - if there is one.

DEFRA has decided on further culls in the Brecon Beacons, and
the NFU is ringing alarm bells.
Not good news.

As part of tough bio-security intensification in the Thirsk
(North Yorkshire) region, all milk tanker deliveries or collections
are to be accompanied by a DEFRA official to ensure cleansing and
disinfection requirements are met in full from 1st August. Clearly,
there are suspicions that milk tankers have been spreading the
disease by failing to carry out disinfection properly.

Farmers at the NFU Sheep Conference at Warwick got a severe
talking to from DEFRA Food and Farming Minister Lord Whitty:

"The cost of FMD has been huge. The government has taken steps
to control the spiralling costs and eliminate abuse of the massive
support paid to contractors and farmers to fight this disease - by
controlling C&D payments, abolishing the standard valuation
card, changing the valuation regime, and reducing payments made
under the LWDS to around 70% of market values. The total cost to
taxpayers of the disease is likely to be over £2 billion. No
other industry would receive that level of support where there was
no direct threat to public health and where the problem had been
compounded by existing trading practices. The Government is
committed to eradicating this disease and we are committed to these
costs. But we must change this system for the future. We need a new
regulatory framework; we need modern industry practices; never again can the taxpayer be obliged to pay
costs which in other industries would be absorbed by the industry
and its insurers.

"I am in the construction, not the demolition, business: we are
here to build a sustainable industry for the future, not destroy
it.

"But there will be no straightforward return to any 'normality'.
Sheep farming will have to change.

Secondary cleansing and disinfection of farms resumed today,
after a two-week halt caused by government concern that costs were
far greater than expected and much higher than in other European
countries.

6th August

An opinion piece from Simon Jenkins, The Times:

Mr Blair is a slow learner at economics. He was surprised to
find that if he offered £1,100 for a cow worth £600 at
market, and £90 for a ewe worth £30, farmers would take
up his offer. If he offered to pay the farmer £1,000 a month
to drive his own tractor cleaning his own farm, he would leap at
it. Any housewife would do the same. Some unscrupulous farmers
would go further. They would infect their flocks and join in the
bonanza. Faced with such stupid government, FMD could spread like
wildfire. It did.

After three months of refusing to believe that
farming is a business, Mr Blair has had enough. Before leaving for
the FMD-endemic shores of South America he produced a familiar
Blair initiative. He promised an army of new officials to go round
trying to work out what every cullable animal is really
“worth” before killing it. Extra auditors will examine
invoices, dockets, pay stubs and reinforce existing red tape. By
the autumn the countryside should have a new ancillary FMD
workforce, over and above farmers, vets and contractors.

Remarkably, within five days of introduction of individual
valuations (30th July), we've got a zero-case day (preceded by a
noticeable decline). The reaction is remarkable as it has appeared
quicker than the usual 8 to 10 day incubating period that ought to
produce a lag between a policy change and a reaction in confirmed
cases. It begs the question whether, now that valuations are more
uncertain, some farmers may be less inclined to report cases - or
indeed hide them. Or maybe the fraudsters were "tipped-off" a few
days before the 30th July announcement.

Jenkins may be a little too cynical in thinking a new industry
of FMD auditors is about to emerge. If it stops fraudsters in their
tracks, and if such are the reason behind the straight line trends,
it could bring a very swift end to FMD.

Zero cases again on the 6th August. Special disinfection
precautions introduced in the Thirsk area of North Yorkshire have
now been extended to the Penrith area (Cumbria). Perhaps indicating
DEFRA has some suspicions of cases that are yet to emerge in the
confirmed case tallies. The show isn't over yet...

Two days with 5 cases make the two zero days look like a false
dawn. Government eventually succumbs to the demands for a public
inquiry and announces no fewer than 3 parallel running Inquiries
into the Foot and Mouth Disease outbreak . Additionally, on 9th
August Animal Health Minister Elliot Morley warned:

"The majority of the livestock sector knows how important it is
to keep up their guard at a time when the disease is confined to a
few hot spots.

"But I am determined that the minority who are flouting these
important measures do not endanger the majority.

"Our checks have revealed a considerable number of
infringements. For the first few days we have just been pointing
this out to farmers and drivers, but we now need to take a harder
line.

" In future farmers and drivers who fail to comply with the
biosecurity requirements are likely to be reported for prosecution.
I am determined that within 30 days there will be no biosecurity
failures within the area under patrol".

Checks in North Yorkshire on 383 vehicles and 677 farms over 5 days
found 43 vehicles (11%) and 46 (7%) farms failing compliance with
bio-security measures.

13th August

The slope of the trend line from 5th July is now giving an
average of 3.6 cases per day. Last few days has produced a few
cases around Powys. Hope it's not the start of something.

16th August

A couple of zero days produces some attenuation in the trend of
daily cases. Figure 12 shows the last week
falling noticeably below the linear trend (hence the last line is
terminated at 8th August). Indeed, the cases since 8th August are
beginning to look like a logistic decline.

18th August

Although the zero days are too few, there is some good news
emerging. Fitting a straight line to the data from 8th August gives
a very similar result to fitting a straight line from 1st August -
with a daily case rate of 2.34 (see updated Figure 12 above). This is half the pre July 5th
line, and two-thirds the rate before 1st August. It clear there has
been an big improvement in the control since the 30th July
announcement of changed valuation policies.

An explanation for the change around 5th July is harder. This
had been preceded by some relaxation in movement controls, and was
introduction of the video education campaign. Were too restrictive
movement controls causing farmers to flout them in an uncontrolled
way that promoted infection more readily than the relaxed controls
? Worth thinking about.

20th August

"The very fact that we are getting ongoing transmission means
that the controls really aren't working", Dr Neil Ferguson

Epidemiologist Dr Neil Ferguson, of Imperial College, London,
whose earlier modelling was promoted and
relied on by MAFF told BBC
Radio 4's Today programme (19th August) that predictions the
epidemic would be over by October were meaningless if security
measures were not imposed more vigorously.

Foot-and-mouth disease has continued longer than expected
because strict movement restrictions and hygiene rules have been
breached, according to experts reported by the BBC.

Dr Ferguson said the epidemic declined faster than expected in
April, partly because of the increased enforcement of restrictions.
Ferguson's expectations were exceeded, but not those of the simpler
logistic model predictions above. Nevertheless, Ferguson offers
this insight into what went wrong:

"Unfortunately, what happened in May was that, for natural
reasons, restrictions had to be lifted in areas where the infection
had not yet been detected, particularly in North Yorkshire and
Lancashire," he said.

"Unfortunately, infection had reached those areas. That caused
the infection to re-establish itself."

He said new infections had been effectively suppressed by culling
but the relaxation of security measures meant new outbreaks were
continuing.

Ferguson does not explain what the "natural reasons" for lifting
the restrictions and relaxing the cull policy were at the end of
April. Was it because Ferguson's model predicted a lesser decline
would still extinguish the epidemic (the
self-fulfilling prophecy argument put here 3rd May ?).

If so, what is so natural about being over-confident and wrong ?
Of course, few people find admission of errors very natural - is
that what was natural about it ?

Or was it like the patient who fails to complete courses of
anti-biotic or other medical treatment because they start feeling
well before the infection is eradicated - and then relapse ; was it
like that natural naivety ?

Was the decision to relax based on misguided interpretations of
modelling from Ferguson, or was it simply a political decision made
for expediency ? Ferguson raised no objections at the time, and to
now dress it up as "natural reasons" suggests an unwillingness to
admit to a mistake and do better next time.

Let's hope the official inquiries take some time to consider
just what role scientific advice and naive overconfidence played in
this decision, and what can be learned from it for the future.

28th August

11 cases in 4 days in Northumberland, and an ongoing daily trend
in Cumbria, have DEFRA ringing alarm bells and promptly imposing
strong restrictions in Northumberland - including 24 hour police
patrols to enforce the restrictions. There's a very worrying upward
kick in daily case trends (see Figure
12.)

31st August

The trend continues at 2.4 cases per day since 1st August, in
spite of two zero days. These were followed by a 5 day - 3 of which
were in Northumberland. One Northumberland case was well outside
the blue box area established around earlier Northumberland cases.
Serious enough to see DEFRA calling in Army assistance, suggesting
to many that DEFRA is now expecting much worse to come. Or is it
just that a month of an unchanged trend has forced DEFRA to respond
with some stronger action ? Sterner action is clearly warranted
whilever the average daily case rate trends along at a constant
rate.

On the basis of the reaction's evident in Figure 12 to previous
policy crackdowns, we might expect the daily case rate to fall to
1.2 per day. It'll take a further crackdown - Figure 12 predicts it
will be 4 weeks coming, to see another halving to 0.6 per day. It's
hard to say just when this will truncate to zero, but it looks like
there's a few months to run still; of course, let's hope I get egg
on my face and it finishes sooner...

8th September

Trend continues at 2.4 cases per day since 1st August, but
there's a hint of a decline in the last few days. Perhaps the army
assistance is beginning to take effect.

Professor David King said "one or two" similar clusters were
likely as farmers fight the tail of the disease in the UK.

King seems intent on making excuses or self-fulfilling
prophecies for the failure to eradicate FMD quickly.

Curiously, he went on to make excuses for failing to use
vaccination - blaming farmers for not accepting suggestions he made
for implementing vaccination as a supplement to culling in Cumbria.
But farmers say vaccinated animals can still carry the virus and
pass it on, without showing any symptoms - so jabs could worsen the
outbreak in the long run.

Of course, what England needs is action, not excuses, and
certainly no more self-fulfilling prophecies. Is King the man who's
going to deliver this ?

16th September

From 8th September, the straight line trend has fallen to 1.17
per day. Remarkably close to my
conjecture of 31st August. This suggests that bringing in the
Army has been effective at halving the daily case rate. What does
DEFRA have to do to halve it again, and why is it waiting til next
month before doing it ?

The debate on Vaccination has rolled on over the last week. The
challenge for farmers and DEFRA who don't think vaccination is a
solution is to think of something better, and do it quickly.
Once-a-month policy wins aren't eradicating FMD quickly enough.

24th September

The trend has been maintained at 1.14 cases per day. Figure 12 has been updated to show a trend line
from 1st September. The series of three trend lines makes it
tempting to believe that something logistical is now appearing.
But...

Nothing appears to be happening to nail the lid on the fmd
coffin. Comparison with the 1967 tail shows no grounds for
confidence or complacency that the end is nigh.

6th October

Figure 14 - The End Phase ?

Remarkably, by the 6th October, there had been a strong run of
zero-case days - suggesting that the outbreak may well be at an
end. The tailing off now evident in the daily case rate, see Figure
14 above, suggests a near logistic decline has finally emerged.
Figure 14 shows a logistic fit to the data from 7th July; actual
stats over the last few days look better than the logistic would
predict.

On the 5th of October,
BBC news reported that two detailed scientific assessments
(published in the leading scientific journals Nature and Science)
had concluded that a more aggressive culling policy should have
been followed earlier in the outbreak. Roy Anderson (Imperial
College) and colleague Neil Ferguson report that resistance from
MAFF and vets prevented this being achieved. Ferguson claimed that
"had the policy been implemented from April, we believe case
numbers would have been reduced by 20%". At least a million fewer
animals would have been slaughtered.

In response to these reports, Prof King, the chief scientific
adviser, tried to claim the epidemic was under control by the end
of April. The facts (as per graphs above) disagree ! Nevertheless
King conceded complacency by vets, farmers, and the public, had
prolonged the outbreak. It seems it was everbody's fault except
MAFF's or his !

The BBC also reported studies by Dr Matt Keeling (Cambridge)
that early adoption of vaccinatin in combination with culling may
have reduced slaughter numbers by 20%, but that late adoption
(early May) would have made only 1 or 2% diffference.

These retrospective studies show the need to make good decisions
early, and to follow them through with effective implementation. It
was evident to this site's author that control was not effective by
the end of April. Why did it take so long for the scientists to
start shouting that the emperor's had no clothes ?

No doubt we will learn more of this as the wisdom of hindsight
catches up with the slow learners.

16th October

No cases since 30th September. That's a pretty good sign that at
last it's over.

"All the statistical analysis, the surveys,
the expenditure forecasting, the projected growth of demand - these
did not lead to the choice at all: they were initiated and selected
in order to bolster it up afterwards"

-Antony Jay, author of the popular BBC television series "Yes
Minister",
in "Householder's Guide to Community Defence Against Bureaucratic
Aggression"

Always worth bearing in mind that even
if you don't have an explicit model, these days many tend to use
computers, there is always a model involved when people perform
actions with the expectation of some change in the future. Human
beings are good at this, indeed it is a built-in ability. Strangely
it comes with a sanity saving feature to ensure most people don't
give-in in desperate situations. To check this feature simply
approach someone who has just done something blindingly stupid and
ask "why did you do that?". In nearly all cases you will not get
the response "because I'm a complete halfwit" Of course this is why
engineers, project managers, etc. get people to state explicitly
what they are going to do, before they do it and hopefully ensure
that halfwittedness is designed out, rather than designed in. Just
because after the event someone can give a good reason for doing
something, it doesn't mean they had any real grasp of what they
were doing at the time. Refining models could just be 'covering
tracks.'

>>
> >> I was too intrigued to wait so I paid my 5 dollars
US in the early hours
> >> of this morning[1]! I am hoping some of the more
skilled analysts on UBA
> >> are reading it at this very moment as it is
stretching my own powers of
> >> analysis!
> >
> >Talk about obtuse writing style... astonishing how many
times I've had
> >to re-read 2 1/2 pages of text. And I'm still not certain
I follow all
> >their reasoning :-(
>
> Usually this means they aren't very clear about their
reasoning either,
> and I am not joking.

A musical point of view expressing depth of feelings (not
mine) ...

Foot & Mouth - Pie in the Sky

They're turning our pigs into pie in the sky
They're piling lives high - selling cheap
The cattle are lowering price as they fry
Mint sauce is too late for the sheep

... lots more snipped ...

recorded version - was AVAILABLE FOR FREE
DOWNLOAD - http://www.mp3.com/CharlottePetersRock - maybe gone now.

Army's Role

Press reports indicate MAFF called for immediate assistance from
the army on 13th March. By 15th, the government announced a
"slaughter on suspicion policy" and the army was providing
logistical support. The government took pains to explain the Army
was not involved in the slaughter - just disposal (20th March). By
28th March, consideration was being given to contingency plans to
have the Army assist with the slaughter.

In 1967 the armed forces were called in
after 12 days. This time contacts were established between MAFF and
the MOD on the day the outbreak was detected, and close contact was
maintained between officials to ensure that possible armed forces
contributions were identified and explored. Since 1967 the size of
the Royal Army Veterinary Service has reduced significantly. The
military vets who could be made available were deployed on 12
March. By then it had also been agreed that military marksmen would
be deployed for rapid culling of pigs in open fields, an essential
contingency in view of the particular virulence of the disease in
these animals. Army logistic experts were deployed to MAFF
headquarters on 15 March. Logistic teams were deployed to MAFF
regional headquarters early the following week"

So MAFF spend 20 days talking to the army before deciding they
needed its help. Why don't they describe how quickly army people
were deployed in 1967, so that readers know they're
comparing apples with apples ? And note the confusion between
MAFF's agreement that the army would be involved in slaughter, and
government press releases to the contrary.

Over the Easter weekend, the calls for use of vaccination gained
momentum. Vaccination is a complex issue, not the least of which is
considering how you'd manage the transition from culling to
vaccination. It may be much worse than changing horses midstream,
if the end is as close as Figure 1 suggests. It may take up to two
weeks to implement a vaccination program, and each vaccinated
animal can still be at risk or a source of risk for up to a week.
Would it really be worthwhile if you'd have to continue the culling
strategy to the point where total elimination ought be well in
sight

Could you be sure that vaccination was managed any more
effectively than the culling campaigns ? Then what about the
often-cited worries about getting from the vaccinated control state
to the disease-free state needed to resume exports, and farmer's
concerns of consumer resistance to FMD affected products. See the
National Farmer's Union (link ref was
"http://www.nfu.org.uk/pr/4018095/pr1704.htm", gone by Mar 2004) 17th April press
release for a summary of the doubts over vaccination.

By 18th April, BBC News reported that the Prime Minister Tony
Blair had thrown his weight behind a limited vaccination program -
even recognising that the cull would have to continue. The NFU and
many of its members remained unconvinced about vaccination, and
supportive of the cull policy.

No vaccination campaign ensued. As the "tail" persisted with new
outbreaks in North Yorkshire and Northumberland in late August,
calls for vaccination were renewed. However, FMD vaccines are not
long-lasting (needing renewal every 6 months), and farmers and
officials remain unconvinced that vaccination is a better
option.

If it is true that farmers have been careless about FMD
disinfection etc.,., or worse have deliberately spread the disease,
it really does bear thinking about how you would implement a
comprehensive vaccination program. Perhaps some of the failures of
the culling program, and particularly the failures in disinfection,
can be attributed to farmers taking short-cuts to gain a
competitive or cost advantage. Our highly competitive market world
provides strong rewards for this, and little to reward cooperative
action. There is a great temptation to free-load on the good
efforts of others. So perhaps some farmers would fail to vaccinate
effectively in the hope that sufficient others have done so and
they will have no need for it. This would frustrate eradication of
FMD as surely as the flouting of disinfection and movement
restrictions have done.